Question

PLAYSTOP6The volume of the solid iscubic feet. Use the formula V = Bh. All angles are 90°.9 ft.6 ft.ft.3 ft.2 ft.2ft.

Answer 1

Volumen of A Solid

Given a solid with a shape of a constant base B and height H, the volume is:

V = BH

The height of the solid is 1 1/4 ft. We need to calculate the area of the base.

The base consists of a larger rectangle from which has been taken a smaller rectangle.

The larger rectangle has dimensions of 9 ft by 6 ft, thus its area is:

A1 = 9 ft * 6 ft = 54 square ft

The smaller rectangle has dimensions of 2 1/2 ft by 4 ft.

The second dimension was calculated as the difference between 9 ft and 2 ft plus 3 ft. (9 ft - 3 ft - 2 ft = 4 ft).

The area of the smaller rectangle is:

A2 = 2 1/2 * 4

The mixed fraction 2 1/2 is converted to improper fraction:

2 1/2 = 2 + 1/2 = 5/2

Thus, the area is:

A2 = 5/2 * 4

A2 = 10 square feet

The area of the base is A1 - A2 = 54 square feet - 10 square feet = 44 square feet

B = 44 square feet.

Now for the volume:

V = 44 square feet * 1 1/4 feet

Again the mixed fraction is converted to a single fraction:

1 1/4 = 1 + 1/4 = 5/4

V = 44 square feet * 5/4 feet

V = 55 cubic feet